Nonmonotonic confining potential and eigenvalue density transition for generalized random matrix model
| Autor: | Khandker Muttalib, Swapnil Yadav, Kazi Alam, Dong Wang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
FOS: Physical sciences Conductance Disordered Systems and Neural Networks (cond-mat.dis-nn) Mathematical Physics (math-ph) Condensed Matter - Disordered Systems and Neural Networks Flory–Huggins solution theory 01 natural sciences 010305 fluids & plasmas Conductor Distribution (mathematics) Joint probability distribution 0103 physical sciences Exponent 010306 general physics Random matrix Mathematical Physics Eigenvalues and eigenvectors 82B44 82D30 60B20 Mathematical physics |
| Zdroj: | Physical review. E. 103(4-1) |
| ISSN: | 2470-0053 |
| Popis: | We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent $\gamma$ (called the $\gamma$-ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with $\gamma=1$ (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the $\gamma$-ensembles. It enables us to numerically compute the eigenvalue density of $\gamma$-ensembles for all $\gamma > 0$. We show that one important effect of the two-particle interaction parameter $\gamma$ is to generate or enhance the non-monotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing $\gamma$ can lead to a large non-monotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of $\gamma$-ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances. Comment: 11 pages, 13 figures |
| Databáze: | OpenAIRE |
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